A block copolymer of a polyolefin and a polymer of a vinyl compound is expected to have better dye-affinity, hydrophilicity, adhesive ability and the like, while retaining the good properties of a polyolefin. Thus, various methods for producing block copolymers have been proposed. For example, one process comprises polymerizing olefins in the presence of a stereospecific catalyst to form polyolefins, and thereafter copolymerizing vinyl compounds and polyolefins in the presence of an alkylene oxide has been proposed (Japanese Patent Publication Gazette No. 8679/1969). However, by this process an alkylene oxide may be incorporated into the copolymer and thus this process is not advantageous.